Merge pull request #2072 from iFrogHop2Worlds/master

A program to calculate double digitial option price

Program's_Contributed_By_Contributors/C++/.vscode/settings.json

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+    "C_Cpp.errorSquiggles": "Disabled"
+}

Program's_Contributed_By_Contributors/C++/.vscode/tasks.json

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+            "label": "C/C++: cl.exe build active file",
+            "command": "cl.exe",
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+                "/EHsc",
+                "/nologo",
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+            "detail": "Task generated by Debugger."
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+            "type": "cppbuild",
+            "label": "C/C++: g++.exe build active file",
+            "command": "C:\\msys64\\mingw64\\bin\\g++.exe",
+            "args": [
+                "-fdiagnostics-color=always",
+                "-g",
+                "${file}",
+                "-o",
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+                "cwd": "${fileDirname}"
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+                "$gcc"
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+            "detail": "Task generated by Debugger."
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Program's_Contributed_By_Contributors/C++/doubleDigitalPriceOption.cpp

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+#include <vector>
+#include <algorithm>
+#include <cmath>
+#include <iostream>
+// A program to calcuate double digital price options
+// read more here https://www.quantstart.com/articles/Double-digital-option-pricing-with-C-via-Monte-Carlo-methods/
+using namespace std;
+
+// random start
+double getOneGaussianBySummation(){
+    double result = 0;
+    for(unsigned int j = 0; j < 12; j++) 
+        result += rand()/static_cast<double>(RAND_MAX);
+
+    result -= 6.0;
+
+    return result;
+}
+
+double gaussian_box_muller() {
+  double x = 0.0;
+  double y = 0.0;
+  double euclid_sq = 0.0;1
+  do {
+    x = 2.0 * rand() / static_cast<double>(RAND_MAX)-1;
+    y = 2.0 * rand() / static_cast<double>(RAND_MAX)-1;
+    euclid_sq = x*x + y*y;
+  } while (euclid_sq >= 1.0);
+
+  return x*sqrt(-2*log(euclid_sq)/euclid_sq);
+}
+
+void calc_path_spot_prices(
+  std::vector<double>& spot_prices,
+  const double& r, // risk free rate
+  const double& v, // volatility
+  const double& T  // Time
+) {
+  double dt = T/static_cast<double>(spot_prices.size());
+  double drift = exp(dt*(r-0.5*v*v));
+  double vol = sqrt(v*v*dt);
+
+  for(int i = 1; i < spot_prices.size(); i++){
+    double gauss_bm = gaussian_box_muller();
+    spot_prices[i] = spot_prices[i-1] * drift * exp(vol*gauss_bm);
+  }
+}
+// random end
+// payoff start
+class PayOff {
+    public:
+        PayOff(){};
+
+        virtual double operator()(double Spot) const = 0;
+
+        virtual PayOff* clone() const = 0;
+
+        virtual ~PayOff(){}
+    private:
+
+};
+
+class PayOffCall : public PayOff {
+    private:
+        double Strike;
+    public:
+        PayOffCall(double Strike_) : Strike(Strike_){};
+
+        virtual double operator()(double Spot) const{
+            return std::max(Spot - Strike, 0.0);
+        };
+
+        virtual ~PayOffCall(){}
+
+        virtual PayOff* clone() const{
+            return new PayOffCall(*this);
+        };
+};
+
+class PayOffPut : public PayOff {
+    private:
+        double Strike;
+    public:
+        PayOffPut(double Strike_) : Strike(Strike_){};
+
+        virtual double operator()(double Spot) const{
+            return std::max(Strike-Spot, 0.0);
+        };
+
+        virtual ~PayOffPut(){}
+
+        virtual PayOff* clone() const{
+            return new PayOffPut(*this);
+        };
+};
+
+// payoff end
+// simple monte carlo start
+double SimpleMonteCarlo(
+    PayOff& thePayOff, 
+    double Expiry,
+    double Spot,
+    double Vol,
+    double r,
+    unsigned long NumberOfPaths
+    ){
+        double variance = Vol*Vol*Expiry;
+        double rootVariance = sqrt(variance);
+        double itoCorrection = -0.5*variance;
+
+        double movedSpot = Spot * exp(r*Expiry +itoCorrection);
+        double thisSpot;
+        double runningSum = 0.0;
+
+        for(unsigned long i=0; i < NumberOfPaths; i++) {
+            double thisGaussian = gaussian_box_muller();
+            thisSpot = movedSpot * exp(rootVariance * thisGaussian);
+            runningSum += thePayOff(thisSpot);
+
+        }
+        double mean = runningSum / NumberOfPaths;
+        mean *= exp(-r*Expiry);
+        return mean;
+    }
+// simple monte carlo end
+// doubledigital start
+class PODoubleDigital : public PayOff {
+    private:
+        double LowerLevel;
+        double UpperLevel;
+    public:
+        PODoubleDigital(double _lowerLevel, double _upperLevel) 
+            : LowerLevel(_lowerLevel), UpperLevel(_upperLevel){
+
+            };
+
+        virtual ~PODoubleDigital(){};
+
+        virtual double operator()(double Spot) const {
+             if(Spot <= LowerLevel)
+                return 0;
+            if(Spot >= UpperLevel)
+                return 0;
+
+            return 1;
+        };
+
+        virtual PayOff* clone() const {
+             return new PODoubleDigital(*this);
+        }
+};
+// doubledigital end
+// main 
+int main(){
+    double Expiry;
+    double Low, Up;
+    double Spot;
+    double Vol;
+    double r;
+    unsigned long NumberOfPaths;
+
+    cout << "\nEnter expiry\n";
+    cin >> Expiry;
+    cout << "\nEnter Low\n";
+    cin >> Low;
+    cout << "\nEnter Up\n";
+    cin >> Up;
+    cout << "\nEnter Spot\n";
+    cin >> Spot;
+    cout << "\nEnter Vol\n";
+    cin >> Vol;
+    cout << "\nEnter r\n";
+    cin >> r;
+    cout << "\nEnter number of paths\n";
+    cin >> NumberOfPaths;
+
+    PODoubleDigital thePayOff(Low, Up);
+
+    double result = SimpleMonteCarlo(
+        thePayOff,
+        Expiry,
+        Spot,
+        Vol,
+        r,
+        NumberOfPaths
+    );
+
+    cout << "\nThe price is " << result << "\n";
+    double tmp;
+    cin >> tmp;
+
+    return 0;
+}